LMFDB - Embedded newform 5054.2.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.90211$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.90211 q^{3} +1.00000 q^{4} -1.79360 q^{5} +2.90211 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.42226 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.90211 q^{3} +1.00000 q^{4} -1.79360 q^{5} +2.90211 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.42226 q^{9} -1.79360 q^{10} +3.35114 q^{11} +2.90211 q^{12} -4.69572 q^{13} +1.00000 q^{14} -5.20524 q^{15} +1.00000 q^{16} +0.891491 q^{17} +5.42226 q^{18} -1.79360 q^{20} +2.90211 q^{21} +3.35114 q^{22} -1.35114 q^{23} +2.90211 q^{24} -1.78298 q^{25} -4.69572 q^{26} +7.02967 q^{27} +1.00000 q^{28} +6.80423 q^{29} -5.20524 q^{30} +8.14475 q^{31} +1.00000 q^{32} +9.72539 q^{33} +0.891491 q^{34} -1.79360 q^{35} +5.42226 q^{36} +9.68915 q^{37} -13.6275 q^{39} -1.79360 q^{40} +0.564101 q^{41} +2.90211 q^{42} -2.20524 q^{43} +3.35114 q^{44} -9.72539 q^{45} -1.35114 q^{46} +12.4211 q^{47} +2.90211 q^{48} +1.00000 q^{49} -1.78298 q^{50} +2.58721 q^{51} -4.69572 q^{52} -9.84452 q^{53} +7.02967 q^{54} -6.01062 q^{55} +1.00000 q^{56} +6.80423 q^{58} -3.47684 q^{59} -5.20524 q^{60} +9.50181 q^{61} +8.14475 q^{62} +5.42226 q^{63} +1.00000 q^{64} +8.42226 q^{65} +9.72539 q^{66} +9.86942 q^{67} +0.891491 q^{68} -3.92116 q^{69} -1.79360 q^{70} +12.4105 q^{71} +5.42226 q^{72} -9.18910 q^{73} +9.68915 q^{74} -5.17442 q^{75} +3.35114 q^{77} -13.6275 q^{78} -12.1436 q^{79} -1.79360 q^{80} +4.13412 q^{81} +0.564101 q^{82} +9.06154 q^{83} +2.90211 q^{84} -1.59898 q^{85} -2.20524 q^{86} +19.7466 q^{87} +3.35114 q^{88} -4.82984 q^{89} -9.72539 q^{90} -4.69572 q^{91} -1.35114 q^{92} +23.6370 q^{93} +12.4211 q^{94} +2.90211 q^{96} -17.0853 q^{97} +1.00000 q^{98} +18.1708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 2 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 2 q^{18} + 2 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 4 q^{24} - 4 q^{25} - 2 q^{26} + 10 q^{27} + 4 q^{28} + 12 q^{29} + 2 q^{30} + 14 q^{31} + 4 q^{32} + 4 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 24 q^{37} - 12 q^{39} + 2 q^{40} + 4 q^{42} + 14 q^{43} + 4 q^{44} - 4 q^{45} + 4 q^{46} - 2 q^{47} + 4 q^{48} + 4 q^{49} - 4 q^{50} - 8 q^{51} - 2 q^{52} + 10 q^{54} - 18 q^{55} + 4 q^{56} + 12 q^{58} + 2 q^{59} + 2 q^{60} + 2 q^{61} + 14 q^{62} + 2 q^{63} + 4 q^{64} + 14 q^{65} + 4 q^{66} + 22 q^{67} + 2 q^{68} + 4 q^{69} + 2 q^{70} + 4 q^{71} + 2 q^{72} + 10 q^{73} + 24 q^{74} + 16 q^{75} + 4 q^{77} - 12 q^{78} + 2 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{84} - 14 q^{85} + 14 q^{86} + 32 q^{87} + 4 q^{88} + 10 q^{89} - 4 q^{90} - 2 q^{91} + 4 q^{92} + 14 q^{93} - 2 q^{94} + 4 q^{96} - 22 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 2 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 2 * q^18 + 2 * q^20 + 4 * q^21 + 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 + 10 * q^27 + 4 * q^28 + 12 * q^29 + 2 * q^30 + 14 * q^31 + 4 * q^32 + 4 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 24 * q^37 - 12 * q^39 + 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 + 4 * q^46 - 2 * q^47 + 4 * q^48 + 4 * q^49 - 4 * q^50 - 8 * q^51 - 2 * q^52 + 10 * q^54 - 18 * q^55 + 4 * q^56 + 12 * q^58 + 2 * q^59 + 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 + 14 * q^65 + 4 * q^66 + 22 * q^67 + 2 * q^68 + 4 * q^69 + 2 * q^70 + 4 * q^71 + 2 * q^72 + 10 * q^73 + 24 * q^74 + 16 * q^75 + 4 * q^77 - 12 * q^78 + 2 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^84 - 14 * q^85 + 14 * q^86 + 32 * q^87 + 4 * q^88 + 10 * q^89 - 4 * q^90 - 2 * q^91 + 4 * q^92 + 14 * q^93 - 2 * q^94 + 4 * q^96 - 22 * q^97 + 4 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.90211	1.67554	0.837768	−	0.546027i	$-0.183860\pi$
$3$	2.90211	1.67554	0.837768	+	0.546027i	$0.183860\pi$
$4$	1.00000	0.500000
$5$	−1.79360	−0.802124	−0.401062	−	0.916051i	$-0.631359\pi$
$5$	−1.79360	−0.802124	−0.401062	+	0.916051i	$0.631359\pi$
$6$	2.90211	1.18478
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	5.42226	1.80742
$10$	−1.79360	−0.567188
$11$	3.35114	1.01041	0.505204	−	0.863000i	$-0.331417\pi$
$11$	3.35114	1.01041	0.505204	+	0.863000i	$0.331417\pi$
$12$	2.90211	0.837768
$13$	−4.69572	−1.30236	−0.651179	−	0.758924i	$-0.725725\pi$
$13$	−4.69572	−1.30236	−0.651179	+	0.758924i	$0.725725\pi$
$14$	1.00000	0.267261
$15$	−5.20524	−1.34399
$16$	1.00000	0.250000
$17$	0.891491	0.216218	0.108109	−	0.994139i	$-0.465520\pi$
$17$	0.891491	0.216218	0.108109	+	0.994139i	$0.465520\pi$
$18$	5.42226	1.27804
$19$	0	0
$19$	0	0
$20$	−1.79360	−0.401062
$21$	2.90211	0.633293
$22$	3.35114	0.714466
$23$	−1.35114	−0.281732	−0.140866	−	0.990029i	$-0.544989\pi$
$23$	−1.35114	−0.281732	−0.140866	+	0.990029i	$0.544989\pi$
$24$	2.90211	0.592391
$25$	−1.78298	−0.356597
$26$	−4.69572	−0.920906
$27$	7.02967	1.35286
$28$	1.00000	0.188982
$29$	6.80423	1.26351	0.631757	−	0.775167i	$-0.282334\pi$
$29$	6.80423	1.26351	0.631757	+	0.775167i	$0.282334\pi$
$30$	−5.20524	−0.950343
$31$	8.14475	1.46284	0.731420	−	0.681928i	$-0.238858\pi$
$31$	8.14475	1.46284	0.731420	+	0.681928i	$0.238858\pi$
$32$	1.00000	0.176777
$33$	9.72539	1.69297
$34$	0.891491	0.152890
$35$	−1.79360	−0.303174
$36$	5.42226	0.903710
$37$	9.68915	1.59289	0.796443	−	0.604713i	$-0.206712\pi$
$37$	9.68915	1.59289	0.796443	+	0.604713i	$0.206712\pi$
$38$	0	0
$39$	−13.6275	−2.18215
$40$	−1.79360	−0.283594
$41$	0.564101	0.0880978	0.0440489	−	0.999029i	$-0.485974\pi$
$41$	0.564101	0.0880978	0.0440489	+	0.999029i	$0.485974\pi$
$42$	2.90211	0.447806
$43$	−2.20524	−0.336296	−0.168148	−	0.985762i	$-0.553779\pi$
$43$	−2.20524	−0.336296	−0.168148	+	0.985762i	$0.553779\pi$
$44$	3.35114	0.505204
$45$	−9.72539	−1.44978
$46$	−1.35114	−0.199215
$47$	12.4211	1.81180	0.905902	−	0.423487i	$-0.139194\pi$
$47$	12.4211	1.81180	0.905902	+	0.423487i	$0.139194\pi$
$48$	2.90211	0.418884
$49$	1.00000	0.142857
$50$	−1.78298	−0.252152
$51$	2.58721	0.362282
$52$	−4.69572	−0.651179
$53$	−9.84452	−1.35225	−0.676124	−	0.736787i	$-0.736342\pi$
$53$	−9.84452	−1.35225	−0.676124	+	0.736787i	$0.736342\pi$
$54$	7.02967	0.956617
$55$	−6.01062	−0.810472
$56$	1.00000	0.133631
$57$	0	0
$58$	6.80423	0.893439
$59$	−3.47684	−0.452645	−0.226323	−	0.974052i	$-0.572670\pi$
$59$	−3.47684	−0.452645	−0.226323	+	0.974052i	$0.572670\pi$
$60$	−5.20524	−0.671994
$61$	9.50181	1.21658	0.608291	−	0.793714i	$-0.291855\pi$
$61$	9.50181	1.21658	0.608291	+	0.793714i	$0.291855\pi$
$62$	8.14475	1.03438
$63$	5.42226	0.683141
$64$	1.00000	0.125000
$65$	8.42226	1.04465
$66$	9.72539	1.19711
$67$	9.86942	1.20574	0.602871	−	0.797839i	$-0.294023\pi$
$67$	9.86942	1.20574	0.602871	+	0.797839i	$0.294023\pi$
$68$	0.891491	0.108109
$69$	−3.92116	−0.472053
$70$	−1.79360	−0.214377
$71$	12.4105	1.47285	0.736427	−	0.676517i	$-0.236512\pi$
$71$	12.4105	1.47285	0.736427	+	0.676517i	$0.236512\pi$
$72$	5.42226	0.639019
$73$	−9.18910	−1.07550	−0.537751	−	0.843104i	$-0.680726\pi$
$73$	−9.18910	−1.07550	−0.537751	+	0.843104i	$0.680726\pi$
$74$	9.68915	1.12634
$75$	−5.17442	−0.597490
$76$	0	0
$77$	3.35114	0.381898
$78$	−13.6275	−1.54301
$79$	−12.1436	−1.36626	−0.683130	−	0.730296i	$-0.739382\pi$
$79$	−12.1436	−1.36626	−0.683130	+	0.730296i	$0.739382\pi$
$80$	−1.79360	−0.200531
$81$	4.13412	0.459347
$82$	0.564101	0.0622945
$83$	9.06154	0.994633	0.497316	−	0.867569i	$-0.334319\pi$
$83$	9.06154	0.994633	0.497316	+	0.867569i	$0.334319\pi$
$84$	2.90211	0.316646
$85$	−1.59898	−0.173434
$86$	−2.20524	−0.237797
$87$	19.7466	2.11706
$88$	3.35114	0.357233
$89$	−4.82984	−0.511962	−0.255981	−	0.966682i	$-0.582398\pi$
$89$	−4.82984	−0.511962	−0.255981	+	0.966682i	$0.582398\pi$
$90$	−9.72539	−1.02515
$91$	−4.69572	−0.492245
$92$	−1.35114	−0.140866
$93$	23.6370	2.45104
$94$	12.4211	1.28114
$95$	0	0
$96$	2.90211	0.296196
$97$	−17.0853	−1.73475	−0.867374	−	0.497657i	$-0.834194\pi$
$97$	−17.0853	−1.73475	−0.867374	+	0.497657i	$0.834194\pi$
$98$	1.00000	0.101015
$99$	18.1708	1.82623
$100$	−1.78298	−0.178298
$101$	−5.14410	−0.511857	−0.255929	−	0.966696i	$-0.582381\pi$
$101$	−5.14410	−0.511857	−0.255929	+	0.966696i	$0.582381\pi$
$102$	2.58721	0.256172
$103$	3.43590	0.338549	0.169275	−	0.985569i	$-0.445858\pi$
$103$	3.43590	0.338549	0.169275	+	0.985569i	$0.445858\pi$
$104$	−4.69572	−0.460453
$105$	−5.20524	−0.507980
$106$	−9.84452	−0.956184
$107$	−19.4530	−1.88059	−0.940295	−	0.340361i	$-0.889451\pi$
$107$	−19.4530	−1.88059	−0.940295	+	0.340361i	$0.889451\pi$
$108$	7.02967	0.676431
$109$	13.5564	1.29847	0.649233	−	0.760590i	$-0.275090\pi$
$109$	13.5564	1.29847	0.649233	+	0.760590i	$0.275090\pi$
$110$	−6.01062	−0.573090
$111$	28.1190	2.66894
$112$	1.00000	0.0944911
$113$	9.40102	0.884373	0.442187	−	0.896923i	$-0.354203\pi$
$113$	9.40102	0.884373	0.442187	+	0.896923i	$0.354203\pi$
$114$	0	0
$115$	2.42341	0.225984
$116$	6.80423	0.631757
$117$	−25.4614	−2.35391
$118$	−3.47684	−0.320069
$119$	0.891491	0.0817229
$120$	−5.20524	−0.475171
$121$	0.230146	0.0209224
$122$	9.50181	0.860253
$123$	1.63708	0.147611
$124$	8.14475	0.731420
$125$	12.1660	1.08816
$126$	5.42226	0.483053
$127$	12.0095	1.06567	0.532834	−	0.846220i	$-0.321127\pi$
$127$	12.0095	1.06567	0.532834	+	0.846220i	$0.321127\pi$
$128$	1.00000	0.0883883
$129$	−6.39986	−0.563477
$130$	8.42226	0.738681
$131$	−11.5557	−1.00962	−0.504812	−	0.863229i	$-0.668438\pi$
$131$	−11.5557	−1.00962	−0.504812	+	0.863229i	$0.668438\pi$
$132$	9.72539	0.846487
$133$	0	0
$134$	9.86942	0.852588
$135$	−12.6085	−1.08516
$136$	0.891491	0.0764448
$137$	−13.7045	−1.17085	−0.585426	−	0.810726i	$-0.699073\pi$
$137$	−13.7045	−1.17085	−0.585426	+	0.810726i	$0.699073\pi$
$138$	−3.92116	−0.333792
$139$	−13.5635	−1.15044	−0.575219	−	0.818000i	$-0.695083\pi$
$139$	−13.5635	−1.15044	−0.575219	+	0.818000i	$0.695083\pi$
$140$	−1.79360	−0.151587
$141$	36.0475	3.03574
$142$	12.4105	1.04146
$143$	−15.7360	−1.31591
$144$	5.42226	0.451855
$145$	−12.2041	−1.01349
$146$	−9.18910	−0.760495
$147$	2.90211	0.239362
$148$	9.68915	0.796443
$149$	−15.0901	−1.23623	−0.618113	−	0.786089i	$-0.712103\pi$
$149$	−15.0901	−1.23623	−0.618113	+	0.786089i	$0.712103\pi$
$150$	−5.17442	−0.422489
$151$	4.55284	0.370505	0.185252	−	0.982691i	$-0.440690\pi$
$151$	4.55284	0.370505	0.185252	+	0.982691i	$0.440690\pi$
$152$	0	0
$153$	4.83390	0.390798
$154$	3.35114	0.270043
$155$	−14.6085	−1.17338
$156$	−13.6275	−1.09107
$157$	−16.5237	−1.31873	−0.659367	−	0.751821i	$-0.729176\pi$
$157$	−16.5237	−1.31873	−0.659367	+	0.751821i	$0.729176\pi$
$158$	−12.1436	−0.966092
$159$	−28.5699	−2.26574
$160$	−1.79360	−0.141797
$161$	−1.35114	−0.106485
$162$	4.13412	0.324807
$163$	−1.74258	−0.136489	−0.0682445	−	0.997669i	$-0.521740\pi$
$163$	−1.74258	−0.136489	−0.0682445	+	0.997669i	$0.521740\pi$
$164$	0.564101	0.0440489
$165$	−17.4435	−1.35797
$166$	9.06154	0.703312
$167$	−14.7697	−1.14292	−0.571458	−	0.820631i	$-0.693622\pi$
$167$	−14.7697	−1.14292	−0.571458	+	0.820631i	$0.693622\pi$
$168$	2.90211	0.223903
$169$	9.04976	0.696136
$170$	−1.59898	−0.122636
$171$	0	0
$172$	−2.20524	−0.168148
$173$	8.10434	0.616161	0.308081	−	0.951360i	$-0.400313\pi$
$173$	8.10434	0.616161	0.308081	+	0.951360i	$0.400313\pi$
$174$	19.7466	1.49699
$175$	−1.78298	−0.134781
$176$	3.35114	0.252602
$177$	−10.0902	−0.758424
$178$	−4.82984	−0.362012
$179$	−23.0710	−1.72441	−0.862204	−	0.506561i	$-0.830916\pi$
$179$	−23.0710	−1.72441	−0.862204	+	0.506561i	$0.830916\pi$
$180$	−9.72539	−0.724888
$181$	−20.9974	−1.56072	−0.780361	−	0.625329i	$-0.784965\pi$
$181$	−20.9974	−1.56072	−0.780361	+	0.625329i	$0.784965\pi$
$182$	−4.69572	−0.348070
$183$	27.5753	2.03843
$184$	−1.35114	−0.0996074
$185$	−17.3785	−1.27769
$186$	23.6370	1.73315
$187$	2.98751	0.218469
$188$	12.4211	0.905902
$189$	7.02967	0.511333
$190$	0	0
$191$	−1.04622	−0.0757015	−0.0378508	−	0.999283i	$-0.512051\pi$
$191$	−1.04622	−0.0757015	−0.0378508	+	0.999283i	$0.512051\pi$
$192$	2.90211	0.209442
$193$	17.1151	1.23197	0.615985	−	0.787758i	$-0.288758\pi$
$193$	17.1151	1.23197	0.615985	+	0.787758i	$0.288758\pi$
$194$	−17.0853	−1.22665
$195$	24.4424	1.75035
$196$	1.00000	0.0714286
$197$	20.0841	1.43094	0.715468	−	0.698646i	$-0.246214\pi$
$197$	20.0841	1.43094	0.715468	+	0.698646i	$0.246214\pi$
$198$	18.1708	1.29134
$199$	−23.1916	−1.64401	−0.822005	−	0.569481i	$-0.807144\pi$
$199$	−23.1916	−1.64401	−0.822005	+	0.569481i	$0.807144\pi$
$200$	−1.78298	−0.126076
$201$	28.6422	2.02026
$202$	−5.14410	−0.361938
$203$	6.80423	0.477563
$204$	2.58721	0.181141
$205$	−1.01177	−0.0706654
$206$	3.43590	0.239390
$207$	−7.32624	−0.509209
$208$	−4.69572	−0.325589
$209$	0	0
$210$	−5.20524	−0.359196
$211$	10.7557	0.740453	0.370227	−	0.928941i	$-0.379280\pi$
$211$	10.7557	0.740453	0.370227	+	0.928941i	$0.379280\pi$
$212$	−9.84452	−0.676124
$213$	36.0166	2.46782
$214$	−19.4530	−1.32978
$215$	3.95533	0.269752
$216$	7.02967	0.478309
$217$	8.14475	0.552901
$218$	13.5564	0.918154
$219$	−26.6678	−1.80204
$220$	−6.01062	−0.405236
$221$	−4.18619	−0.281594
$222$	28.1190	1.88722
$223$	−25.0911	−1.68022	−0.840112	−	0.542413i	$-0.817511\pi$
$223$	−25.0911	−1.68022	−0.840112	+	0.542413i	$0.817511\pi$
$224$	1.00000	0.0668153
$225$	−9.66780	−0.644520
$226$	9.40102	0.625346
$227$	6.25261	0.415000	0.207500	−	0.978235i	$-0.433467\pi$
$227$	6.25261	0.415000	0.207500	+	0.978235i	$0.433467\pi$
$228$	0	0
$229$	−2.97438	−0.196553	−0.0982764	−	0.995159i	$-0.531333\pi$
$229$	−2.97438	−0.196553	−0.0982764	+	0.995159i	$0.531333\pi$
$230$	2.42341	0.159795
$231$	9.72539	0.639884
$232$	6.80423	0.446719
$233$	1.95385	0.128001	0.0640006	−	0.997950i	$-0.479614\pi$
$233$	1.95385	0.128001	0.0640006	+	0.997950i	$0.479614\pi$
$234$	−25.4614	−1.66446
$235$	−22.2786	−1.45329
$236$	−3.47684	−0.226323
$237$	−35.2421	−2.28922
$238$	0.891491	0.0577868
$239$	1.26470	0.0818067	0.0409033	−	0.999163i	$-0.486976\pi$
$239$	1.26470	0.0818067	0.0409033	+	0.999163i	$0.486976\pi$
$240$	−5.20524	−0.335997
$241$	3.03373	0.195420	0.0977098	−	0.995215i	$-0.468848\pi$
$241$	3.03373	0.195420	0.0977098	+	0.995215i	$0.468848\pi$
$242$	0.230146	0.0147943
$243$	−9.09132	−0.583209
$244$	9.50181	0.608291
$245$	−1.79360	−0.114589
$246$	1.63708	0.104377
$247$	0	0
$248$	8.14475	0.517192
$249$	26.2976	1.66654
$250$	12.1660	0.769445
$251$	21.3548	1.34790	0.673950	−	0.738777i	$-0.264596\pi$
$251$	21.3548	1.34790	0.673950	+	0.738777i	$0.264596\pi$
$252$	5.42226	0.341570
$253$	−4.52786	−0.284664
$254$	12.0095	0.753541
$255$	−4.64043	−0.290595
$256$	1.00000	0.0625000
$257$	12.8208	0.799738	0.399869	−	0.916572i	$-0.369056\pi$
$257$	12.8208	0.799738	0.399869	+	0.916572i	$0.369056\pi$
$258$	−6.39986	−0.398438
$259$	9.68915	0.602055
$260$	8.42226	0.522326
$261$	36.8943	2.28370
$262$	−11.5557	−0.713912
$263$	20.0534	1.23655	0.618274	−	0.785963i	$-0.287832\pi$
$263$	20.0534	1.23655	0.618274	+	0.785963i	$0.287832\pi$
$264$	9.72539	0.598556
$265$	17.6572	1.08467
$266$	0	0
$267$	−14.0167	−0.857811
$268$	9.86942	0.602871
$269$	6.88140	0.419566	0.209783	−	0.977748i	$-0.432724\pi$
$269$	6.88140	0.419566	0.209783	+	0.977748i	$0.432724\pi$
$270$	−12.6085	−0.767326
$271$	−7.46371	−0.453388	−0.226694	−	0.973966i	$-0.572792\pi$
$271$	−7.46371	−0.453388	−0.226694	+	0.973966i	$0.572792\pi$
$272$	0.891491	0.0540546
$273$	−13.6275	−0.824774
$274$	−13.7045	−0.827918
$275$	−5.97503	−0.360308
$276$	−3.92116	−0.236026
$277$	16.3701	0.983583	0.491791	−	0.870713i	$-0.336342\pi$
$277$	16.3701	0.983583	0.491791	+	0.870713i	$0.336342\pi$
$278$	−13.5635	−0.813482
$279$	44.1629	2.64397
$280$	−1.79360	−0.107188
$281$	7.36865	0.439577	0.219789	−	0.975548i	$-0.429463\pi$
$281$	7.36865	0.439577	0.219789	+	0.975548i	$0.429463\pi$
$282$	36.0475	2.14659
$283$	3.61854	0.215100	0.107550	−	0.994200i	$-0.465699\pi$
$283$	3.61854	0.215100	0.107550	+	0.994200i	$0.465699\pi$
$284$	12.4105	0.736427
$285$	0	0
$286$	−15.7360	−0.930490
$287$	0.564101	0.0332978
$288$	5.42226	0.319510
$289$	−16.2052	−0.953250
$290$	−12.2041	−0.716649
$291$	−49.5834	−2.90663
$292$	−9.18910	−0.537751
$293$	−17.2598	−1.00833	−0.504165	−	0.863608i	$-0.668200\pi$
$293$	−17.2598	−1.00833	−0.504165	+	0.863608i	$0.668200\pi$
$294$	2.90211	0.169255
$295$	6.23607	0.363078
$296$	9.68915	0.563171
$297$	23.5574	1.36694
$298$	−15.0901	−0.874144
$299$	6.34458	0.366916
$300$	−5.17442	−0.298745
$301$	−2.20524	−0.127108
$302$	4.55284	0.261986
$303$	−14.9288	−0.857635
$304$	0	0
$305$	−17.0425	−0.975850
$306$	4.83390	0.276336
$307$	0.804339	0.0459060	0.0229530	−	0.999737i	$-0.492693\pi$
$307$	0.804339	0.0459060	0.0229530	+	0.999737i	$0.492693\pi$
$308$	3.35114	0.190949
$309$	9.97137	0.567251
$310$	−14.6085	−0.829704
$311$	−12.1316	−0.687921	−0.343960	−	0.938984i	$-0.611769\pi$
$311$	−12.1316	−0.687921	−0.343960	+	0.938984i	$0.611769\pi$
$312$	−13.6275	−0.771505
$313$	−2.75048	−0.155466	−0.0777330	−	0.996974i	$-0.524768\pi$
$313$	−2.75048	−0.155466	−0.0777330	+	0.996974i	$0.524768\pi$
$314$	−16.5237	−0.932486
$315$	−9.72539	−0.547964
$316$	−12.1436	−0.683130
$317$	19.0806	1.07167	0.535836	−	0.844322i	$-0.319996\pi$
$317$	19.0806	1.07167	0.535836	+	0.844322i	$0.319996\pi$
$318$	−28.5699	−1.60212
$319$	22.8019	1.27666
$320$	−1.79360	−0.100266
$321$	−56.4547	−3.15100
$322$	−1.35114	−0.0752961
$323$	0	0
$324$	4.13412	0.229674
$325$	8.37238	0.464416
$326$	−1.74258	−0.0965124
$327$	39.3422	2.17563
$328$	0.564101	0.0311473
$329$	12.4211	0.684798
$330$	−17.4435	−0.960233
$331$	−17.3760	−0.955071	−0.477536	−	0.878612i	$-0.658470\pi$
$331$	−17.3760	−0.955071	−0.477536	+	0.878612i	$0.658470\pi$
$332$	9.06154	0.497316
$333$	52.5371	2.87902
$334$	−14.7697	−0.808164
$335$	−17.7018	−0.967155
$336$	2.90211	0.158323
$337$	−19.9631	−1.08746	−0.543731	−	0.839260i	$-0.682989\pi$
$337$	−19.9631	−1.08746	−0.543731	+	0.839260i	$0.682989\pi$
$338$	9.04976	0.492242
$339$	27.2828	1.48180
$340$	−1.59898	−0.0867170
$341$	27.2942	1.47806
$342$	0	0
$343$	1.00000	0.0539949
$344$	−2.20524	−0.118899
$345$	7.03302	0.378645
$346$	8.10434	0.435692
$347$	2.16952	0.116466	0.0582329	−	0.998303i	$-0.481453\pi$
$347$	2.16952	0.116466	0.0582329	+	0.998303i	$0.481453\pi$
$348$	19.7466	1.05853
$349$	−1.98938	−0.106489	−0.0532445	−	0.998582i	$-0.516956\pi$
$349$	−1.98938	−0.106489	−0.0532445	+	0.998582i	$0.516956\pi$
$350$	−1.78298	−0.0953044
$351$	−33.0094	−1.76191
$352$	3.35114	0.178616
$353$	−14.4974	−0.771621	−0.385810	−	0.922578i	$-0.626078\pi$
$353$	−14.4974	−0.771621	−0.385810	+	0.922578i	$0.626078\pi$
$354$	−10.0902	−0.536286
$355$	−22.2595	−1.18141
$356$	−4.82984	−0.255981
$357$	2.58721	0.136930
$358$	−23.0710	−1.21934
$359$	1.85055	0.0976685	0.0488343	−	0.998807i	$-0.484449\pi$
$359$	1.85055	0.0976685	0.0488343	+	0.998807i	$0.484449\pi$
$360$	−9.72539	−0.512573
$361$	0	0
$362$	−20.9974	−1.10360
$363$	0.667910	0.0350562
$364$	−4.69572	−0.246122
$365$	16.4816	0.862687
$366$	27.5753	1.44139
$367$	11.5721	0.604059	0.302029	−	0.953299i	$-0.402336\pi$
$367$	11.5721	0.604059	0.302029	+	0.953299i	$0.402336\pi$
$368$	−1.35114	−0.0704331
$369$	3.05870	0.159230
$370$	−17.3785	−0.903466
$371$	−9.84452	−0.511102
$372$	23.6370	1.22552
$373$	6.21939	0.322028	0.161014	−	0.986952i	$-0.448524\pi$
$373$	6.21939	0.322028	0.161014	+	0.986952i	$0.448524\pi$
$374$	2.98751	0.154481
$375$	35.3071	1.82325
$376$	12.4211	0.640570
$377$	−31.9507	−1.64555
$378$	7.02967	0.361567
$379$	−4.13639	−0.212472	−0.106236	−	0.994341i	$-0.533880\pi$
$379$	−4.13639	−0.212472	−0.106236	+	0.994341i	$0.533880\pi$
$380$	0	0
$381$	34.8528	1.78556
$382$	−1.04622	−0.0535291
$383$	−10.4982	−0.536433	−0.268216	−	0.963359i	$-0.586434\pi$
$383$	−10.4982	−0.536433	−0.268216	+	0.963359i	$0.586434\pi$
$384$	2.90211	0.148098
$385$	−6.01062	−0.306330
$386$	17.1151	0.871134
$387$	−11.9574	−0.607829
$388$	−17.0853	−0.867374
$389$	2.12454	0.107719	0.0538593	−	0.998549i	$-0.482848\pi$
$389$	2.12454	0.107719	0.0538593	+	0.998549i	$0.482848\pi$
$390$	24.4424	1.23769
$391$	−1.20453	−0.0609157
$392$	1.00000	0.0505076
$393$	−33.5359	−1.69166
$394$	20.0841	1.01182
$395$	21.7808	1.09591
$396$	18.1708	0.913115
$397$	−7.81310	−0.392128	−0.196064	−	0.980591i	$-0.562816\pi$
$397$	−7.81310	−0.392128	−0.196064	+	0.980591i	$0.562816\pi$
$398$	−23.1916	−1.16249
$399$	0	0
$400$	−1.78298	−0.0891491
$401$	−3.16129	−0.157867	−0.0789336	−	0.996880i	$-0.525152\pi$
$401$	−3.16129	−0.157867	−0.0789336	+	0.996880i	$0.525152\pi$
$402$	28.6422	1.42854
$403$	−38.2454	−1.90514
$404$	−5.14410	−0.255929
$405$	−7.41498	−0.368453
$406$	6.80423	0.337688
$407$	32.4697	1.60946
$408$	2.58721	0.128086
$409$	10.3423	0.511392	0.255696	−	0.966757i	$-0.417695\pi$
$409$	10.3423	0.511392	0.255696	+	0.966757i	$0.417695\pi$
$410$	−1.01177	−0.0499680
$411$	−39.7719	−1.96180
$412$	3.43590	0.169275
$413$	−3.47684	−0.171084
$414$	−7.32624	−0.360065
$415$	−16.2528	−0.797819
$416$	−4.69572	−0.230226
$417$	−39.3627	−1.92760
$418$	0	0
$419$	−12.2298	−0.597466	−0.298733	−	0.954337i	$-0.596564\pi$
$419$	−12.2298	−0.597466	−0.298733	+	0.954337i	$0.596564\pi$
$420$	−5.20524	−0.253990
$421$	37.2441	1.81516	0.907582	−	0.419874i	$-0.137926\pi$
$421$	37.2441	1.81516	0.907582	+	0.419874i	$0.137926\pi$
$422$	10.7557	0.523580
$423$	67.3505	3.27469
$424$	−9.84452	−0.478092
$425$	−1.58951	−0.0771028
$426$	36.0166	1.74501
$427$	9.50181	0.459825
$428$	−19.4530	−0.940295
$429$	−45.6677	−2.20486
$430$	3.95533	0.190743
$431$	14.1672	0.682411	0.341205	−	0.939989i	$-0.389165\pi$
$431$	14.1672	0.682411	0.341205	+	0.939989i	$0.389165\pi$
$432$	7.02967	0.338215
$433$	29.9164	1.43769	0.718844	−	0.695171i	$-0.244672\pi$
$433$	29.9164	1.43769	0.718844	+	0.695171i	$0.244672\pi$
$434$	8.14475	0.390960
$435$	−35.4176	−1.69815
$436$	13.5564	0.649233
$437$	0	0
$438$	−26.6678	−1.27424
$439$	33.8419	1.61519	0.807593	−	0.589740i	$-0.200770\pi$
$439$	33.8419	1.61519	0.807593	+	0.589740i	$0.200770\pi$
$440$	−6.01062	−0.286545
$441$	5.42226	0.258203
$442$	−4.18619	−0.199117
$443$	−27.9903	−1.32986	−0.664930	−	0.746906i	$-0.731539\pi$
$443$	−27.9903	−1.32986	−0.664930	+	0.746906i	$0.731539\pi$
$444$	28.1190	1.33447
$445$	8.66283	0.410657
$446$	−25.0911	−1.18810
$447$	−43.7931	−2.07134
$448$	1.00000	0.0472456
$449$	−10.3380	−0.487881	−0.243940	−	0.969790i	$-0.578440\pi$
$449$	−10.3380	−0.487881	−0.243940	+	0.969790i	$0.578440\pi$
$450$	−9.66780	−0.455744
$451$	1.89038	0.0890146
$452$	9.40102	0.442187
$453$	13.2128	0.620794
$454$	6.25261	0.293450
$455$	8.42226	0.394842
$456$	0	0
$457$	6.97155	0.326115	0.163058	−	0.986617i	$-0.447864\pi$
$457$	6.97155	0.326115	0.163058	+	0.986617i	$0.447864\pi$
$458$	−2.97438	−0.138984
$459$	6.26689	0.292514
$460$	2.42341	0.112992
$461$	20.2741	0.944257	0.472128	−	0.881530i	$-0.343486\pi$
$461$	20.2741	0.944257	0.472128	+	0.881530i	$0.343486\pi$
$462$	9.72539	0.452466
$463$	24.5300	1.14001	0.570003	−	0.821642i	$-0.306942\pi$
$463$	24.5300	1.14001	0.570003	+	0.821642i	$0.306942\pi$
$464$	6.80423	0.315878
$465$	−42.3954	−1.96604
$466$	1.95385	0.0905105
$467$	4.74391	0.219522	0.109761	−	0.993958i	$-0.464991\pi$
$467$	4.74391	0.219522	0.109761	+	0.993958i	$0.464991\pi$
$468$	−25.4614	−1.17695
$469$	9.86942	0.455728
$470$	−22.2786	−1.02763
$471$	−47.9536	−2.20959
$472$	−3.47684	−0.160034
$473$	−7.39008	−0.339796
$474$	−35.2421	−1.61872
$475$	0	0
$476$	0.891491	0.0408614
$477$	−53.3795	−2.44408
$478$	1.26470	0.0578461
$479$	−33.1590	−1.51507	−0.757536	−	0.652793i	$-0.773597\pi$
$479$	−33.1590	−1.51507	−0.757536	+	0.652793i	$0.773597\pi$
$480$	−5.20524	−0.237586
$481$	−45.4975	−2.07451
$482$	3.03373	0.138183
$483$	−3.92116	−0.178419
$484$	0.230146	0.0104612
$485$	30.6442	1.39148
$486$	−9.09132	−0.412391
$487$	−29.1633	−1.32151	−0.660757	−	0.750600i	$-0.729764\pi$
$487$	−29.1633	−1.32151	−0.660757	+	0.750600i	$0.729764\pi$
$488$	9.50181	0.430127
$489$	−5.05715	−0.228692
$490$	−1.79360	−0.0810268
$491$	−28.2609	−1.27540	−0.637699	−	0.770286i	$-0.720114\pi$
$491$	−28.2609	−1.27540	−0.637699	+	0.770286i	$0.720114\pi$
$492$	1.63708	0.0738055
$493$	6.06591	0.273195
$494$	0	0
$495$	−32.5912	−1.46486
$496$	8.14475	0.365710
$497$	12.4105	0.556686
$498$	26.2976	1.17842
$499$	14.0615	0.629481	0.314740	−	0.949178i	$-0.398083\pi$
$499$	14.0615	0.629481	0.314740	+	0.949178i	$0.398083\pi$
$500$	12.1660	0.544080
$501$	−42.8635	−1.91500
$502$	21.3548	0.953109
$503$	−2.11160	−0.0941514	−0.0470757	−	0.998891i	$-0.514990\pi$
$503$	−2.11160	−0.0941514	−0.0470757	+	0.998891i	$0.514990\pi$
$504$	5.42226	0.241527
$505$	9.22649	0.410573
$506$	−4.52786	−0.201288
$507$	26.2634	1.16640
$508$	12.0095	0.532834
$509$	−40.4069	−1.79100	−0.895502	−	0.445057i	$-0.853183\pi$
$509$	−40.4069	−1.79100	−0.895502	+	0.445057i	$0.853183\pi$
$510$	−4.64043	−0.205482
$511$	−9.18910	−0.406502
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.8208	0.565500
$515$	−6.16264	−0.271559
$516$	−6.39986	−0.281738
$517$	41.6249	1.83066
$518$	9.68915	0.425717
$519$	23.5197	1.03240
$520$	8.42226	0.369341
$521$	−2.75704	−0.120788	−0.0603941	−	0.998175i	$-0.519236\pi$
$521$	−2.75704	−0.120788	−0.0603941	+	0.998175i	$0.519236\pi$
$522$	36.8943	1.61482
$523$	−29.2105	−1.27729	−0.638644	−	0.769502i	$-0.720504\pi$
$523$	−29.2105	−1.27729	−0.638644	+	0.769502i	$0.720504\pi$
$524$	−11.5557	−0.504812
$525$	−5.17442	−0.225830
$526$	20.0534	0.874371
$527$	7.26097	0.316293
$528$	9.72539	0.423243
$529$	−21.1744	−0.920627
$530$	17.6572	0.766979
$531$	−18.8523	−0.818120
$532$	0	0
$533$	−2.64886	−0.114735
$534$	−14.0167	−0.606564
$535$	34.8909	1.50847
$536$	9.86942	0.426294
$537$	−66.9547	−2.88931
$538$	6.88140	0.296678
$539$	3.35114	0.144344
$540$	−12.6085	−0.542581
$541$	4.75442	0.204408	0.102204	−	0.994763i	$-0.467410\pi$
$541$	4.75442	0.204408	0.102204	+	0.994763i	$0.467410\pi$
$542$	−7.46371	−0.320594
$543$	−60.9368	−2.61505
$544$	0.891491	0.0382224
$545$	−24.3148	−1.04153
$546$	−13.6275	−0.583203
$547$	−25.4236	−1.08704	−0.543518	−	0.839398i	$-0.682908\pi$
$547$	−25.4236	−1.08704	−0.543518	+	0.839398i	$0.682908\pi$
$548$	−13.7045	−0.585426
$549$	51.5213	2.19887
$550$	−5.97503	−0.254776
$551$	0	0
$552$	−3.92116	−0.166896
$553$	−12.1436	−0.516398
$554$	16.3701	0.695498
$555$	−50.4344	−2.14082
$556$	−13.5635	−0.575219
$557$	−40.4579	−1.71426	−0.857128	−	0.515104i	$-0.827753\pi$
$557$	−40.4579	−1.71426	−0.857128	+	0.515104i	$0.827753\pi$
$558$	44.1629	1.86957
$559$	10.3552	0.437978
$560$	−1.79360	−0.0757936
$561$	8.67010	0.366052
$562$	7.36865	0.310828
$563$	−5.84361	−0.246279	−0.123139	−	0.992389i	$-0.539296\pi$
$563$	−5.84361	−0.246279	−0.123139	+	0.992389i	$0.539296\pi$
$564$	36.0475	1.51787
$565$	−16.8617	−0.709377
$566$	3.61854	0.152099
$567$	4.13412	0.173617
$568$	12.4105	0.520732
$569$	45.9324	1.92559	0.962793	−	0.270240i	$-0.0871032\pi$
$569$	45.9324	1.92559	0.962793	+	0.270240i	$0.0871032\pi$
$570$	0	0
$571$	1.11880	0.0468204	0.0234102	−	0.999726i	$-0.492548\pi$
$571$	1.11880	0.0468204	0.0234102	+	0.999726i	$0.492548\pi$
$572$	−15.7360	−0.657956
$573$	−3.03624	−0.126841
$574$	0.564101	0.0235451
$575$	2.40906	0.100465
$576$	5.42226	0.225928
$577$	−1.14127	−0.0475116	−0.0237558	−	0.999718i	$-0.507562\pi$
$577$	−1.14127	−0.0475116	−0.0237558	+	0.999718i	$0.507562\pi$
$578$	−16.2052	−0.674049
$579$	49.6699	2.06421
$580$	−12.2041	−0.506747
$581$	9.06154	0.375936
$582$	−49.5834	−2.05530
$583$	−32.9904	−1.36632
$584$	−9.18910	−0.380248
$585$	45.6677	1.88813
$586$	−17.2598	−0.712997
$587$	7.53245	0.310898	0.155449	−	0.987844i	$-0.450318\pi$
$587$	7.53245	0.310898	0.155449	+	0.987844i	$0.450318\pi$
$588$	2.90211	0.119681
$589$	0	0
$590$	6.23607	0.256735
$591$	58.2864	2.39758
$592$	9.68915	0.398222
$593$	−39.5912	−1.62582	−0.812909	−	0.582391i	$-0.802117\pi$
$593$	−39.5912	−1.62582	−0.812909	+	0.582391i	$0.802117\pi$
$594$	23.5574	0.966573
$595$	−1.59898	−0.0655519
$596$	−15.0901	−0.618113
$597$	−67.3047	−2.75460
$598$	6.34458	0.259449
$599$	−9.09975	−0.371806	−0.185903	−	0.982568i	$-0.559521\pi$
$599$	−9.09975	−0.371806	−0.185903	+	0.982568i	$0.559521\pi$
$600$	−5.17442	−0.211245
$601$	47.3923	1.93317	0.966586	−	0.256343i	$-0.0825176\pi$
$601$	47.3923	1.93317	0.966586	+	0.256343i	$0.0825176\pi$
$602$	−2.20524	−0.0898790
$603$	53.5146	2.17928
$604$	4.55284	0.185252
$605$	−0.412791	−0.0167823
$606$	−14.9288	−0.606440
$607$	−11.0559	−0.448744	−0.224372	−	0.974504i	$-0.572033\pi$
$607$	−11.0559	−0.448744	−0.224372	+	0.974504i	$0.572033\pi$
$608$	0	0
$609$	19.7466	0.800174
$610$	−17.0425	−0.690030
$611$	−58.3260	−2.35962
$612$	4.83390	0.195399
$613$	−13.1861	−0.532582	−0.266291	−	0.963893i	$-0.585798\pi$
$613$	−13.1861	−0.532582	−0.266291	+	0.963893i	$0.585798\pi$
$614$	0.804339	0.0324605
$615$	−2.93628	−0.118402
$616$	3.35114	0.135021
$617$	−22.5269	−0.906899	−0.453450	−	0.891282i	$-0.649807\pi$
$617$	−22.5269	−0.906899	−0.453450	+	0.891282i	$0.649807\pi$
$618$	9.97137	0.401107
$619$	−15.8939	−0.638829	−0.319415	−	0.947615i	$-0.603486\pi$
$619$	−15.8939	−0.638829	−0.319415	+	0.947615i	$0.603486\pi$
$620$	−14.6085	−0.586690
$621$	−9.49808	−0.381145
$622$	−12.1316	−0.486434
$623$	−4.82984	−0.193504
$624$	−13.6275	−0.545537
$625$	−12.9061	−0.516242
$626$	−2.75048	−0.109931
$627$	0	0
$628$	−16.5237	−0.659367
$629$	8.63780	0.344412
$630$	−9.72539	−0.387469
$631$	−28.7031	−1.14265	−0.571326	−	0.820723i	$-0.693571\pi$
$631$	−28.7031	−1.14265	−0.571326	+	0.820723i	$0.693571\pi$
$632$	−12.1436	−0.483046
$633$	31.2143	1.24066
$634$	19.0806	0.757787
$635$	−21.5402	−0.854798
$636$	−28.5699	−1.13287
$637$	−4.69572	−0.186051
$638$	22.8019	0.902737
$639$	67.2929	2.66207
$640$	−1.79360	−0.0708984
$641$	33.1457	1.30918	0.654588	−	0.755986i	$-0.272842\pi$
$641$	33.1457	1.30918	0.654588	+	0.755986i	$0.272842\pi$
$642$	−56.4547	−2.22809
$643$	−41.0673	−1.61954	−0.809769	−	0.586749i	$-0.800408\pi$
$643$	−41.0673	−1.61954	−0.809769	+	0.586749i	$0.800408\pi$
$644$	−1.35114	−0.0532424
$645$	11.4788	0.451978
$646$	0	0
$647$	−18.9104	−0.743446	−0.371723	−	0.928344i	$-0.621233\pi$
$647$	−18.9104	−0.743446	−0.371723	+	0.928344i	$0.621233\pi$
$648$	4.13412	0.162404
$649$	−11.6514	−0.457356
$650$	8.37238	0.328392
$651$	23.6370	0.926406
$652$	−1.74258	−0.0682445
$653$	−22.5316	−0.881728	−0.440864	−	0.897574i	$-0.645328\pi$
$653$	−22.5316	−0.881728	−0.440864	+	0.897574i	$0.645328\pi$
$654$	39.3422	1.53840
$655$	20.7263	0.809844
$656$	0.564101	0.0220244
$657$	−49.8257	−1.94388
$658$	12.4211	0.484225
$659$	−21.5790	−0.840598	−0.420299	−	0.907386i	$-0.638075\pi$
$659$	−21.5790	−0.840598	−0.420299	+	0.907386i	$0.638075\pi$
$660$	−17.4435	−0.678987
$661$	−2.48714	−0.0967386	−0.0483693	−	0.998830i	$-0.515402\pi$
$661$	−2.48714	−0.0967386	−0.0483693	+	0.998830i	$0.515402\pi$
$662$	−17.3760	−0.675337
$663$	−12.1488	−0.471820
$664$	9.06154	0.351656
$665$	0	0
$666$	52.5371	2.03577
$667$	−9.19347	−0.355973
$668$	−14.7697	−0.571458
$669$	−72.8172	−2.81528
$670$	−17.7018	−0.683882
$671$	31.8419	1.22924
$672$	2.90211	0.111951
$673$	24.4626	0.942962	0.471481	−	0.881876i	$-0.343720\pi$
$673$	24.4626	0.942962	0.471481	+	0.881876i	$0.343720\pi$
$674$	−19.9631	−0.768951
$675$	−12.5338	−0.482426
$676$	9.04976	0.348068
$677$	−18.5981	−0.714785	−0.357392	−	0.933954i	$-0.616334\pi$
$677$	−18.5981	−0.714785	−0.357392	+	0.933954i	$0.616334\pi$
$678$	27.2828	1.04779
$679$	−17.0853	−0.655673
$680$	−1.59898	−0.0613182
$681$	18.1458	0.695348
$682$	27.2942	1.04515
$683$	−14.4508	−0.552945	−0.276473	−	0.961022i	$-0.589166\pi$
$683$	−14.4508	−0.552945	−0.276473	+	0.961022i	$0.589166\pi$
$684$	0	0
$685$	24.5804	0.939169
$686$	1.00000	0.0381802
$687$	−8.63200	−0.329331
$688$	−2.20524	−0.0840741
$689$	46.2271	1.76111
$690$	7.03302	0.267742
$691$	−0.0947999	−0.00360636	−0.00180318	−	0.999998i	$-0.500574\pi$
$691$	−0.0947999	−0.00360636	−0.00180318	+	0.999998i	$0.500574\pi$
$692$	8.10434	0.308081
$693$	18.1708	0.690250
$694$	2.16952	0.0823537
$695$	24.3275	0.922794
$696$	19.7466	0.748494
$697$	0.502891	0.0190484
$698$	−1.98938	−0.0752991
$699$	5.67030	0.214471
$700$	−1.78298	−0.0673904
$701$	32.4918	1.22720	0.613599	−	0.789618i	$-0.289721\pi$
$701$	32.4918	1.22720	0.613599	+	0.789618i	$0.289721\pi$
$702$	−33.0094	−1.24586
$703$	0	0
$704$	3.35114	0.126301
$705$	−64.6549	−2.43504
$706$	−14.4974	−0.545618
$707$	−5.14410	−0.193464
$708$	−10.0902	−0.379212
$709$	18.5243	0.695694	0.347847	−	0.937551i	$-0.386913\pi$
$709$	18.5243	0.695694	0.347847	+	0.937551i	$0.386913\pi$
$710$	−22.2595	−0.835384
$711$	−65.8457	−2.46941
$712$	−4.82984	−0.181006
$713$	−11.0047	−0.412129
$714$	2.58721	0.0968239
$715$	28.2242	1.05552
$716$	−23.0710	−0.862204
$717$	3.67030	0.137070
$718$	1.85055	0.0690621
$719$	−17.0122	−0.634446	−0.317223	−	0.948351i	$-0.602750\pi$
$719$	−17.0122	−0.634446	−0.317223	+	0.948351i	$0.602750\pi$
$720$	−9.72539	−0.362444
$721$	3.43590	0.127960
$722$	0	0
$723$	8.80423	0.327433
$724$	−20.9974	−0.780361
$725$	−12.1318	−0.450564
$726$	0.667910	0.0247885
$727$	−25.8492	−0.958694	−0.479347	−	0.877625i	$-0.659127\pi$
$727$	−25.8492	−0.958694	−0.479347	+	0.877625i	$0.659127\pi$
$728$	−4.69572	−0.174035
$729$	−38.7864	−1.43653
$730$	16.4816	0.610012
$731$	−1.96596	−0.0727135
$732$	27.5753	1.01921
$733$	50.0046	1.84696	0.923481	−	0.383645i	$-0.125331\pi$
$733$	50.0046	1.84696	0.923481	+	0.383645i	$0.125331\pi$
$734$	11.5721	0.427134
$735$	−5.20524	−0.191998
$736$	−1.35114	−0.0498037
$737$	33.0738	1.21829
$738$	3.05870	0.112592
$739$	47.1280	1.73363	0.866815	−	0.498629i	$-0.166163\pi$
$739$	47.1280	1.73363	0.866815	+	0.498629i	$0.166163\pi$
$740$	−17.3785	−0.638847
$741$	0	0
$742$	−9.84452	−0.361404
$743$	28.9368	1.06159	0.530794	−	0.847501i	$-0.321894\pi$
$743$	28.9368	1.06159	0.530794	+	0.847501i	$0.321894\pi$
$744$	23.6370	0.866573
$745$	27.0656	0.991607
$746$	6.21939	0.227708
$747$	49.1340	1.79772
$748$	2.98751	0.109234
$749$	−19.4530	−0.710796
$750$	35.3071	1.28923
$751$	−2.18974	−0.0799047	−0.0399524	−	0.999202i	$-0.512721\pi$
$751$	−2.18974	−0.0799047	−0.0399524	+	0.999202i	$0.512721\pi$
$752$	12.4211	0.452951
$753$	61.9739	2.25846
$754$	−31.9507	−1.16358
$755$	−8.16599	−0.297191
$756$	7.02967	0.255667
$757$	1.42350	0.0517381	0.0258690	−	0.999665i	$-0.491765\pi$
$757$	1.42350	0.0517381	0.0258690	+	0.999665i	$0.491765\pi$
$758$	−4.13639	−0.150240
$759$	−13.1404	−0.476965
$760$	0	0
$761$	−10.5898	−0.383881	−0.191941	−	0.981407i	$-0.561478\pi$
$761$	−10.5898	−0.383881	−0.191941	+	0.981407i	$0.561478\pi$
$762$	34.8528	1.26259
$763$	13.5564	0.490774
$764$	−1.04622	−0.0378508
$765$	−8.67010	−0.313468
$766$	−10.4982	−0.379315
$767$	16.3262	0.589506
$768$	2.90211	0.104721
$769$	31.8457	1.14839	0.574193	−	0.818720i	$-0.305316\pi$
$769$	31.8457	1.14839	0.574193	+	0.818720i	$0.305316\pi$
$770$	−6.01062	−0.216608
$771$	37.2073	1.33999
$772$	17.1151	0.615985
$773$	−9.88076	−0.355386	−0.177693	−	0.984086i	$-0.556863\pi$
$773$	−9.88076	−0.355386	−0.177693	+	0.984086i	$0.556863\pi$
$774$	−11.9574	−0.429800
$775$	−14.5219	−0.521644
$776$	−17.0853	−0.613326
$777$	28.1190	1.00876
$778$	2.12454	0.0761685
$779$	0	0
$780$	24.4424	0.875177
$781$	41.5893	1.48818
$782$	−1.20453	−0.0430739
$783$	47.8315	1.70936
$784$	1.00000	0.0357143
$785$	29.6370	1.05779
$786$	−33.5359	−1.19618
$787$	45.6161	1.62604	0.813019	−	0.582238i	$-0.197823\pi$
$787$	45.6161	1.62604	0.813019	+	0.582238i	$0.197823\pi$
$788$	20.0841	0.715468
$789$	58.1973	2.07188
$790$	21.7808	0.774926
$791$	9.40102	0.334262
$792$	18.1708	0.645670
$793$	−44.6178	−1.58442
$794$	−7.81310	−0.277276
$795$	51.2431	1.81741
$796$	−23.1916	−0.822005
$797$	25.4225	0.900513	0.450256	−	0.892899i	$-0.351333\pi$
$797$	25.4225	0.900513	0.450256	+	0.892899i	$0.351333\pi$
$798$	0	0
$799$	11.0733	0.391746
$800$	−1.78298	−0.0630380
$801$	−26.1887	−0.925331
$802$	−3.16129	−0.111629
$803$	−30.7940	−1.08670
$804$	28.6422	1.01013
$805$	2.42341	0.0854141
$806$	−38.2454	−1.34714
$807$	19.9706	0.702998
$808$	−5.14410	−0.180969
$809$	−37.9113	−1.33289	−0.666444	−	0.745555i	$-0.732185\pi$
$809$	−37.9113	−1.33289	−0.666444	+	0.745555i	$0.732185\pi$
$810$	−7.41498	−0.260536
$811$	47.0115	1.65080	0.825399	−	0.564550i	$-0.190950\pi$
$811$	47.0115	1.65080	0.825399	+	0.564550i	$0.190950\pi$
$812$	6.80423	0.238782
$813$	−21.6605	−0.759668
$814$	32.4697	1.13806
$815$	3.12549	0.109481
$816$	2.58721	0.0905704
$817$	0	0
$818$	10.3423	0.361609
$819$	−25.4614	−0.889693
$820$	−1.01177	−0.0353327
$821$	−22.9452	−0.800792	−0.400396	−	0.916342i	$-0.631127\pi$
$821$	−22.9452	−0.800792	−0.400396	+	0.916342i	$0.631127\pi$
$822$	−39.7719	−1.38721
$823$	18.5489	0.646573	0.323287	−	0.946301i	$-0.395212\pi$
$823$	18.5489	0.646573	0.323287	+	0.946301i	$0.395212\pi$
$824$	3.43590	0.119695
$825$	−17.3402	−0.603708
$826$	−3.47684	−0.120975
$827$	−21.6261	−0.752015	−0.376007	−	0.926617i	$-0.622703\pi$
$827$	−21.6261	−0.752015	−0.376007	+	0.926617i	$0.622703\pi$
$828$	−7.32624	−0.254604
$829$	41.5932	1.44459	0.722296	−	0.691584i	$-0.243087\pi$
$829$	41.5932	1.44459	0.722296	+	0.691584i	$0.243087\pi$
$830$	−16.2528	−0.564143
$831$	47.5078	1.64803
$832$	−4.69572	−0.162795
$833$	0.891491	0.0308883
$834$	−39.3627	−1.36302
$835$	26.4911	0.916761
$836$	0	0
$837$	57.2549	1.97902
$838$	−12.2298	−0.422472
$839$	21.9798	0.758825	0.379413	−	0.925228i	$-0.376126\pi$
$839$	21.9798	0.758825	0.379413	+	0.925228i	$0.376126\pi$
$840$	−5.20524	−0.179598
$841$	17.2975	0.596465
$842$	37.2441	1.28352
$843$	21.3847	0.736527
$844$	10.7557	0.370227
$845$	−16.2317	−0.558387
$846$	67.3505	2.31556
$847$	0.230146	0.00790791
$848$	−9.84452	−0.338062
$849$	10.5014	0.360408
$850$	−1.58951	−0.0545199
$851$	−13.0914	−0.448768
$852$	36.0166	1.23391
$853$	−16.2957	−0.557955	−0.278978	−	0.960298i	$-0.589996\pi$
$853$	−16.2957	−0.557955	−0.278978	+	0.960298i	$0.589996\pi$
$854$	9.50181	0.325145
$855$	0	0
$856$	−19.4530	−0.664889
$857$	−0.591153	−0.0201934	−0.0100967	−	0.999949i	$-0.503214\pi$
$857$	−0.591153	−0.0201934	−0.0100967	+	0.999949i	$0.503214\pi$
$858$	−45.6677	−1.55907
$859$	−23.0257	−0.785627	−0.392814	−	0.919618i	$-0.628498\pi$
$859$	−23.0257	−0.785627	−0.392814	+	0.919618i	$0.628498\pi$
$860$	3.95533	0.134876
$861$	1.63708	0.0557917
$862$	14.1672	0.482537
$863$	−31.2778	−1.06471	−0.532354	−	0.846522i	$-0.678693\pi$
$863$	−31.2778	−1.06471	−0.532354	+	0.846522i	$0.678693\pi$
$864$	7.02967	0.239154
$865$	−14.5360	−0.494238
$866$	29.9164	1.01660
$867$	−47.0294	−1.59720
$868$	8.14475	0.276451
$869$	−40.6949	−1.38048
$870$	−35.4176	−1.20077
$871$	−46.3440	−1.57031
$872$	13.5564	0.459077
$873$	−92.6409	−3.13542
$874$	0	0
$875$	12.1660	0.411285
$876$	−26.6678	−0.901021
$877$	26.1032	0.881442	0.440721	−	0.897644i	$-0.354723\pi$
$877$	26.1032	0.881442	0.440721	+	0.897644i	$0.354723\pi$
$878$	33.8419	1.14211
$879$	−50.0899	−1.68949
$880$	−6.01062	−0.202618
$881$	−25.4882	−0.858719	−0.429359	−	0.903134i	$-0.641261\pi$
$881$	−25.4882	−0.858719	−0.429359	+	0.903134i	$0.641261\pi$
$882$	5.42226	0.182577
$883$	16.7948	0.565189	0.282594	−	0.959240i	$-0.408805\pi$
$883$	16.7948	0.565189	0.282594	+	0.959240i	$0.408805\pi$
$884$	−4.18619	−0.140797
$885$	18.0978	0.608350
$886$	−27.9903	−0.940353
$887$	17.0461	0.572352	0.286176	−	0.958177i	$-0.407616\pi$
$887$	17.0461	0.572352	0.286176	+	0.958177i	$0.407616\pi$
$888$	28.1190	0.943612
$889$	12.0095	0.402785
$890$	8.66283	0.290379
$891$	13.8540	0.464128
$892$	−25.0911	−0.840112
$893$	0	0
$894$	−43.7931	−1.46466
$895$	41.3803	1.38319
$896$	1.00000	0.0334077
$897$	18.4127	0.614781
$898$	−10.3380	−0.344984
$899$	55.4187	1.84832
$900$	−9.66780	−0.322260
$901$	−8.77631	−0.292381
$902$	1.89038	0.0629428
$903$	−6.39986	−0.212974
$904$	9.40102	0.312673
$905$	37.6610	1.25189
$906$	13.2128	0.438967
$907$	42.8075	1.42140	0.710701	−	0.703495i	$-0.248378\pi$
$907$	42.8075	1.42140	0.710701	+	0.703495i	$0.248378\pi$
$908$	6.25261	0.207500
$909$	−27.8927	−0.925141
$910$	8.42226	0.279195
$911$	−7.44877	−0.246789	−0.123394	−	0.992358i	$-0.539378\pi$
$911$	−7.44877	−0.246789	−0.123394	+	0.992358i	$0.539378\pi$
$912$	0	0
$913$	30.3665	1.00498
$914$	6.97155	0.230598
$915$	−49.4592	−1.63507
$916$	−2.97438	−0.0982764
$917$	−11.5557	−0.381602
$918$	6.26689	0.206838
$919$	−25.8561	−0.852913	−0.426457	−	0.904508i	$-0.640238\pi$
$919$	−25.8561	−0.852913	−0.426457	+	0.904508i	$0.640238\pi$
$920$	2.42341	0.0798975
$921$	2.33428	0.0769172
$922$	20.2741	0.667691
$923$	−58.2761	−1.91818
$924$	9.72539	0.319942
$925$	−17.2756	−0.568018
$926$	24.5300	0.806106
$927$	18.6303	0.611901
$928$	6.80423	0.223360
$929$	−9.94547	−0.326300	−0.163150	−	0.986601i	$-0.552165\pi$
$929$	−9.94547	−0.326300	−0.163150	+	0.986601i	$0.552165\pi$
$930$	−42.3954	−1.39020
$931$	0	0
$932$	1.95385	0.0640006
$933$	−35.2073	−1.15264
$934$	4.74391	0.155226
$935$	−5.35842	−0.175239
$936$	−25.4614	−0.832232
$937$	−27.7372	−0.906136	−0.453068	−	0.891476i	$-0.649671\pi$
$937$	−27.7372	−0.906136	−0.453068	+	0.891476i	$0.649671\pi$
$938$	9.86942	0.322248
$939$	−7.98219	−0.260489
$940$	−22.2786	−0.726646
$941$	28.7406	0.936918	0.468459	−	0.883485i	$-0.344809\pi$
$941$	28.7406	0.936918	0.468459	+	0.883485i	$0.344809\pi$
$942$	−47.9536	−1.56241
$943$	−0.762180	−0.0248200
$944$	−3.47684	−0.113161
$945$	−12.6085	−0.410153
$946$	−7.39008	−0.240272
$947$	8.44215	0.274333	0.137166	−	0.990548i	$-0.456200\pi$
$947$	8.44215	0.274333	0.137166	+	0.990548i	$0.456200\pi$
$948$	−35.2421	−1.14461
$949$	43.1494	1.40069
$950$	0	0
$951$	55.3740	1.79563
$952$	0.891491	0.0288934
$953$	−27.8424	−0.901905	−0.450953	−	0.892548i	$-0.648916\pi$
$953$	−27.8424	−0.901905	−0.450953	+	0.892548i	$0.648916\pi$
$954$	−53.3795	−1.72823
$955$	1.87650	0.0607220
$956$	1.26470	0.0409033
$957$	66.1738	2.13909
$958$	−33.1590	−1.07132
$959$	−13.7045	−0.442541
$960$	−5.20524	−0.167998
$961$	35.3369	1.13990
$962$	−45.4975	−1.46690
$963$	−105.479	−3.39902
$964$	3.03373	0.0977098
$965$	−30.6977	−0.988193
$966$	−3.92116	−0.126161
$967$	10.3678	0.333407	0.166703	−	0.986007i	$-0.446688\pi$
$967$	10.3678	0.333407	0.166703	+	0.986007i	$0.446688\pi$
$968$	0.230146	0.00739717
$969$	0	0
$970$	30.6442	0.983928
$971$	−12.5882	−0.403974	−0.201987	−	0.979388i	$-0.564740\pi$
$971$	−12.5882	−0.403974	−0.201987	+	0.979388i	$0.564740\pi$
$972$	−9.09132	−0.291604
$973$	−13.5635	−0.434825
$974$	−29.1633	−0.934451
$975$	24.2976	0.778146
$976$	9.50181	0.304145
$977$	34.7790	1.11268	0.556340	−	0.830955i	$-0.312205\pi$
$977$	34.7790	1.11268	0.556340	+	0.830955i	$0.312205\pi$
$978$	−5.05715	−0.161710
$979$	−16.1855	−0.517290
$980$	−1.79360	−0.0572946
$981$	73.5062	2.34687
$982$	−28.2609	−0.901842
$983$	−60.1263	−1.91773	−0.958865	−	0.283863i	$-0.908384\pi$
$983$	−60.1263	−1.91773	−0.958865	+	0.283863i	$0.908384\pi$
$984$	1.63708	0.0521884
$985$	−36.0230	−1.14779
$986$	6.06591	0.193178
$987$	36.0475	1.14740
$988$	0	0
$989$	2.97959	0.0947456
$990$	−32.5912	−1.03581
$991$	53.3760	1.69554	0.847772	−	0.530360i	$-0.177943\pi$
$991$	53.3760	1.69554	0.847772	+	0.530360i	$0.177943\pi$
$992$	8.14475	0.258596
$993$	−50.4271	−1.60026
$994$	12.4105	0.393637
$995$	41.5966	1.31870
$996$	26.2976	0.833272
$997$	−19.1868	−0.607652	−0.303826	−	0.952728i	$-0.598264\pi$
$997$	−19.1868	−0.607652	−0.303826	+	0.952728i	$0.598264\pi$
$998$	14.0615	0.445110
$999$	68.1116	2.15495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.y.1.4	yes	4
19.18	odd	2		5054.2.a.v.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.v.1.1	✓	4	19.18	odd	2
5054.2.a.y.1.4	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.90211 q^{3} +1.00000 q^{4} -1.79360 q^{5} +2.90211 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.42226 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.90211 q^{3} +1.00000 q^{4} -1.79360 q^{5} +2.90211 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.42226 q^{9} -1.79360 q^{10} +3.35114 q^{11} +2.90211 q^{12} -4.69572 q^{13} +1.00000 q^{14} -5.20524 q^{15} +1.00000 q^{16} +0.891491 q^{17} +5.42226 q^{18} -1.79360 q^{20} +2.90211 q^{21} +3.35114 q^{22} -1.35114 q^{23} +2.90211 q^{24} -1.78298 q^{25} -4.69572 q^{26} +7.02967 q^{27} +1.00000 q^{28} +6.80423 q^{29} -5.20524 q^{30} +8.14475 q^{31} +1.00000 q^{32} +9.72539 q^{33} +0.891491 q^{34} -1.79360 q^{35} +5.42226 q^{36} +9.68915 q^{37} -13.6275 q^{39} -1.79360 q^{40} +0.564101 q^{41} +2.90211 q^{42} -2.20524 q^{43} +3.35114 q^{44} -9.72539 q^{45} -1.35114 q^{46} +12.4211 q^{47} +2.90211 q^{48} +1.00000 q^{49} -1.78298 q^{50} +2.58721 q^{51} -4.69572 q^{52} -9.84452 q^{53} +7.02967 q^{54} -6.01062 q^{55} +1.00000 q^{56} +6.80423 q^{58} -3.47684 q^{59} -5.20524 q^{60} +9.50181 q^{61} +8.14475 q^{62} +5.42226 q^{63} +1.00000 q^{64} +8.42226 q^{65} +9.72539 q^{66} +9.86942 q^{67} +0.891491 q^{68} -3.92116 q^{69} -1.79360 q^{70} +12.4105 q^{71} +5.42226 q^{72} -9.18910 q^{73} +9.68915 q^{74} -5.17442 q^{75} +3.35114 q^{77} -13.6275 q^{78} -12.1436 q^{79} -1.79360 q^{80} +4.13412 q^{81} +0.564101 q^{82} +9.06154 q^{83} +2.90211 q^{84} -1.59898 q^{85} -2.20524 q^{86} +19.7466 q^{87} +3.35114 q^{88} -4.82984 q^{89} -9.72539 q^{90} -4.69572 q^{91} -1.35114 q^{92} +23.6370 q^{93} +12.4211 q^{94} +2.90211 q^{96} -17.0853 q^{97} +1.00000 q^{98} +18.1708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 2 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 2 q^{18} + 2 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 4 q^{24} - 4 q^{25} - 2 q^{26} + 10 q^{27} + 4 q^{28} + 12 q^{29} + 2 q^{30} + 14 q^{31} + 4 q^{32} + 4 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 24 q^{37} - 12 q^{39} + 2 q^{40} + 4 q^{42} + 14 q^{43} + 4 q^{44} - 4 q^{45} + 4 q^{46} - 2 q^{47} + 4 q^{48} + 4 q^{49} - 4 q^{50} - 8 q^{51} - 2 q^{52} + 10 q^{54} - 18 q^{55} + 4 q^{56} + 12 q^{58} + 2 q^{59} + 2 q^{60} + 2 q^{61} + 14 q^{62} + 2 q^{63} + 4 q^{64} + 14 q^{65} + 4 q^{66} + 22 q^{67} + 2 q^{68} + 4 q^{69} + 2 q^{70} + 4 q^{71} + 2 q^{72} + 10 q^{73} + 24 q^{74} + 16 q^{75} + 4 q^{77} - 12 q^{78} + 2 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{84} - 14 q^{85} + 14 q^{86} + 32 q^{87} + 4 q^{88} + 10 q^{89} - 4 q^{90} - 2 q^{91} + 4 q^{92} + 14 q^{93} - 2 q^{94} + 4 q^{96} - 22 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 2 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 2 * q^18 + 2 * q^20 + 4 * q^21 + 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 + 10 * q^27 + 4 * q^28 + 12 * q^29 + 2 * q^30 + 14 * q^31 + 4 * q^32 + 4 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 24 * q^37 - 12 * q^39 + 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 + 4 * q^46 - 2 * q^47 + 4 * q^48 + 4 * q^49 - 4 * q^50 - 8 * q^51 - 2 * q^52 + 10 * q^54 - 18 * q^55 + 4 * q^56 + 12 * q^58 + 2 * q^59 + 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 + 14 * q^65 + 4 * q^66 + 22 * q^67 + 2 * q^68 + 4 * q^69 + 2 * q^70 + 4 * q^71 + 2 * q^72 + 10 * q^73 + 24 * q^74 + 16 * q^75 + 4 * q^77 - 12 * q^78 + 2 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^84 - 14 * q^85 + 14 * q^86 + 32 * q^87 + 4 * q^88 + 10 * q^89 - 4 * q^90 - 2 * q^91 + 4 * q^92 + 14 * q^93 - 2 * q^94 + 4 * q^96 - 22 * q^97 + 4 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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